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Simplifying (5z + 3)(7 + z) = 0 Reorder the terms: (3 + 5z)(7 + z) = 0 Multiply (3 + 5z) * (7 + z) (3(7 + z) + 5z * (7 + z)) = 0 ((7 * 3 + z * 3) + 5z * (7 + z)) = 0 ((21 + 3z) + 5z * (7 + z)) = 0 (21 + 3z + (7 * 5z + z * 5z)) = 0 (21 + 3z + (35z + 5z2)) = 0 Combine like terms: 3z + 35z = 38z (21 + 38z + 5z2) = 0 Solving 21 + 38z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + z)(3 + 5z) = 0Subproblem 1
Set the factor '(7 + z)' equal to zero and attempt to solve: Simplifying 7 + z = 0 Solving 7 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + z = 0 + -7 z = 0 + -7 Combine like terms: 0 + -7 = -7 z = -7 Simplifying z = -7Subproblem 2
Set the factor '(3 + 5z)' equal to zero and attempt to solve: Simplifying 3 + 5z = 0 Solving 3 + 5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 5z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5z = 0 + -3 5z = 0 + -3 Combine like terms: 0 + -3 = -3 5z = -3 Divide each side by '5'. z = -0.6 Simplifying z = -0.6Solution
z = {-7, -0.6}
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